For the parabola y^2 = 20x, what is the coordinates of the vertex?

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Question: For the parabola y^2 = 20x, what is the coordinates of the vertex?

Options:

Correct Answer: (0, 0)

Solution:

The vertex of the parabola y^2 = 4px is at (0, 0). Here, p = 5, but the vertex remains at (0, 0).

For the parabola y^2 = 20x, what is the coordinates of the vertex?

For the parabola y^2 = 20x, what is the coordinates of the vertex?

Step 1: Identify the equation of the parabola, which is y^2 = 20x.
Step 2: Recognize that this equation is in the form y^2 = 4px, where p is a constant.
Step 3: Compare the equation y^2 = 20x with y^2 = 4px to find p.
Step 4: From the equation, we see that 4p = 20.
Step 5: Solve for p by dividing both sides by 4: p = 20 / 4 = 5.
Step 6: Understand that the vertex of a parabola in this form is always at the point (0, 0).
Step 7: Conclude that the coordinates of the vertex for the parabola y^2 = 20x are (0, 0).

Parabola Vertex – Understanding the standard form of a parabola and identifying its vertex.
Standard Form of Parabola – Recognizing the equation of a parabola in the form y^2 = 4px and its implications.